Recreate water bevel
Here is one way using a Warp Modifier
Your surface must be highly subdivided, it will contain the modifier. In the gif below this is the plane object.
The modifier stack is as follows:

The from and to fields in the warp modifier are the important pieces here.
The modifier pulls from point a to point b, thus creating the effect shown in the gif below. By animating the cube to move toward the empty, as well as the strength parameter of the modifier it exaggerates the effect. This should get you in the direction you are looking for.